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Simplifying 7 = 2x(x + -4) + -3(x + -4) Reorder the terms: 7 = 2x(-4 + x) + -3(x + -4) 7 = (-4 * 2x + x * 2x) + -3(x + -4) 7 = (-8x + 2x2) + -3(x + -4) Reorder the terms: 7 = -8x + 2x2 + -3(-4 + x) 7 = -8x + 2x2 + (-4 * -3 + x * -3) 7 = -8x + 2x2 + (12 + -3x) Reorder the terms: 7 = 12 + -8x + -3x + 2x2 Combine like terms: -8x + -3x = -11x 7 = 12 + -11x + 2x2 Solving 7 = 12 + -11x + 2x2 Solving for variable 'x'. Combine like terms: 7 + -12 = -5 -5 + 11x + -2x2 = 12 + -11x + 2x2 + -12 + 11x + -2x2 Reorder the terms: -5 + 11x + -2x2 = 12 + -12 + -11x + 11x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -5 + 11x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2 -5 + 11x + -2x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -5 + 11x + -2x2 = 0 + 2x2 + -2x2 -5 + 11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 11x + -2x2 = 0 Factor a trinomial. (-5 + x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {5, 0.5}
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