Solve the quadratic by factoring. 3x^(2)+2x-4=-2x Answer: x=

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. 3x^2 + 2x - 4 + 2x = 0 Combine like terms. 3x^2 + 4x - 4 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to (3)(-4) = -12 and add up to 4. The numbers that satisfy these conditions are 6 and -2. 6 * -2 = -12 6 + (-2) = 4Rewrite Middle Term: Rewrite the middle term using the two numbers found in Step 2. 3x^2 + 6x - 2x - 4 = 0Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms. (3x^2 + 6x) - (2x + 4) = 0 Factor out the common factors from each group. 3x(x + 2) - 2(x + 2) = 0Factor Common Binomial: Factor out the common binomial factor. (3x - 2)(x + 2) = 0Set Factors Equal: Set each factor equal to zero and solve for x. 3x - 2 = 0 or x + 2 = 0 For 3x - 2 = 0: 3x = 2 x = 2/3 For x + 2 = 0: x = -2

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Solve the quadratic by factoring.

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3 x^{2}+2 x-4=-2 x

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Answer:

x=

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. $\newline$ $3x^2 + 2x - 4 + 2x = 0$ $\newline$ Combine like terms. $\newline$ $3x^2 + 4x - 4 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $(3)(-4) = -12$ and add up to $4$ . $\newline$ The numbers that satisfy these conditions are $6$ and $-2$ . $\newline$ $6 \times -2 = -12$ $\newline$ $6 + (-2) = 4$
Rewrite Middle Term: Rewrite the middle term using the two numbers found in Step $2$ . $\newline$ $3x^2 + 6x - 2x - 4 = 0$
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(3x^2 + 6x) - (2x + 4) = 0$ $\newline$ Factor out the common factors from each group. $\newline$ $3x(x + 2) - 2(x + 2) = 0$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ $(3x - 2)(x + 2) = 0$
Set Factors Equal: Set each factor equal to zero and solve for $x$ . $3x - 2 = 0$ or $x + 2 = 0$ For $3x - 2 = 0$ : $3x = 2$ $x = \frac{2}{3}$ For $x + 2 = 0$ : $x = -2$