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Simplifying 7x(x + -4) = (2x + 2)(x + -4) Reorder the terms: 7x(-4 + x) = (2x + 2)(x + -4) (-4 * 7x + x * 7x) = (2x + 2)(x + -4) (-28x + 7x2) = (2x + 2)(x + -4) Reorder the terms: -28x + 7x2 = (2 + 2x)(x + -4) Reorder the terms: -28x + 7x2 = (2 + 2x)(-4 + x) Multiply (2 + 2x) * (-4 + x) -28x + 7x2 = (2(-4 + x) + 2x * (-4 + x)) -28x + 7x2 = ((-4 * 2 + x * 2) + 2x * (-4 + x)) -28x + 7x2 = ((-8 + 2x) + 2x * (-4 + x)) -28x + 7x2 = (-8 + 2x + (-4 * 2x + x * 2x)) -28x + 7x2 = (-8 + 2x + (-8x + 2x2)) Combine like terms: 2x + -8x = -6x -28x + 7x2 = (-8 + -6x + 2x2) Solving -28x + 7x2 = -8 + -6x + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -28x + 6x + 7x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2 Combine like terms: -28x + 6x = -22x 8 + -22x + 7x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 8 + -22x + 5x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2 Reorder the terms: 8 + -22x + 5x2 = -8 + 8 + -6x + 6x + 2x2 + -2x2 Combine like terms: -8 + 8 = 0 8 + -22x + 5x2 = 0 + -6x + 6x + 2x2 + -2x2 8 + -22x + 5x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 8 + -22x + 5x2 = 0 + 2x2 + -2x2 8 + -22x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -22x + 5x2 = 0 Factor a trinomial. (2 + -5x)(4 + -1x) = 0Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0.4, 4}
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