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Simplifying 5x(x + -3) + -42 = 4x(x + -1) Reorder the terms: 5x(-3 + x) + -42 = 4x(x + -1) (-3 * 5x + x * 5x) + -42 = 4x(x + -1) (-15x + 5x2) + -42 = 4x(x + -1) Reorder the terms: -42 + -15x + 5x2 = 4x(x + -1) Reorder the terms: -42 + -15x + 5x2 = 4x(-1 + x) -42 + -15x + 5x2 = (-1 * 4x + x * 4x) -42 + -15x + 5x2 = (-4x + 4x2) Solving -42 + -15x + 5x2 = -4x + 4x2 Solving for variable 'x'. Reorder the terms: -42 + -15x + 4x + 5x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: -15x + 4x = -11x -42 + -11x + 5x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 -42 + -11x + 1x2 = -4x + 4x2 + 4x + -4x2 Reorder the terms: -42 + -11x + 1x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -42 + -11x + 1x2 = 0 + 4x2 + -4x2 -42 + -11x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -42 + -11x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(14 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-3, 14}
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