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Simplifying (3x + -4)(x + 2) = (x + 6)(2x + -3) Reorder the terms: (-4 + 3x)(x + 2) = (x + 6)(2x + -3) Reorder the terms: (-4 + 3x)(2 + x) = (x + 6)(2x + -3) Multiply (-4 + 3x) * (2 + x) (-4(2 + x) + 3x * (2 + x)) = (x + 6)(2x + -3) ((2 * -4 + x * -4) + 3x * (2 + x)) = (x + 6)(2x + -3) ((-8 + -4x) + 3x * (2 + x)) = (x + 6)(2x + -3) (-8 + -4x + (2 * 3x + x * 3x)) = (x + 6)(2x + -3) (-8 + -4x + (6x + 3x2)) = (x + 6)(2x + -3) Combine like terms: -4x + 6x = 2x (-8 + 2x + 3x2) = (x + 6)(2x + -3) Reorder the terms: -8 + 2x + 3x2 = (6 + x)(2x + -3) Reorder the terms: -8 + 2x + 3x2 = (6 + x)(-3 + 2x) Multiply (6 + x) * (-3 + 2x) -8 + 2x + 3x2 = (6(-3 + 2x) + x(-3 + 2x)) -8 + 2x + 3x2 = ((-3 * 6 + 2x * 6) + x(-3 + 2x)) -8 + 2x + 3x2 = ((-18 + 12x) + x(-3 + 2x)) -8 + 2x + 3x2 = (-18 + 12x + (-3 * x + 2x * x)) -8 + 2x + 3x2 = (-18 + 12x + (-3x + 2x2)) Combine like terms: 12x + -3x = 9x -8 + 2x + 3x2 = (-18 + 9x + 2x2) Solving -8 + 2x + 3x2 = -18 + 9x + 2x2 Solving for variable 'x'. Reorder the terms: -8 + 18 + 2x + -9x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2 Combine like terms: -8 + 18 = 10 10 + 2x + -9x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2 Combine like terms: 2x + -9x = -7x 10 + -7x + 3x2 + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 10 + -7x + 1x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2 Reorder the terms: 10 + -7x + 1x2 = -18 + 18 + 9x + -9x + 2x2 + -2x2 Combine like terms: -18 + 18 = 0 10 + -7x + 1x2 = 0 + 9x + -9x + 2x2 + -2x2 10 + -7x + 1x2 = 9x + -9x + 2x2 + -2x2 Combine like terms: 9x + -9x = 0 10 + -7x + 1x2 = 0 + 2x2 + -2x2 10 + -7x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 10 + -7x + 1x2 = 0 Factor a trinomial. (2 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2, 5}
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