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Simplifying 7(x + -2)(x + 5) = -10(x + 5) Reorder the terms: 7(-2 + x)(x + 5) = -10(x + 5) Reorder the terms: 7(-2 + x)(5 + x) = -10(x + 5) Multiply (-2 + x) * (5 + x) 7(-2(5 + x) + x(5 + x)) = -10(x + 5) 7((5 * -2 + x * -2) + x(5 + x)) = -10(x + 5) 7((-10 + -2x) + x(5 + x)) = -10(x + 5) 7(-10 + -2x + (5 * x + x * x)) = -10(x + 5) 7(-10 + -2x + (5x + x2)) = -10(x + 5) Combine like terms: -2x + 5x = 3x 7(-10 + 3x + x2) = -10(x + 5) (-10 * 7 + 3x * 7 + x2 * 7) = -10(x + 5) (-70 + 21x + 7x2) = -10(x + 5) Reorder the terms: -70 + 21x + 7x2 = -10(5 + x) -70 + 21x + 7x2 = (5 * -10 + x * -10) -70 + 21x + 7x2 = (-50 + -10x) Solving -70 + 21x + 7x2 = -50 + -10x Solving for variable 'x'. Reorder the terms: -70 + 50 + 21x + 10x + 7x2 = -50 + -10x + 50 + 10x Combine like terms: -70 + 50 = -20 -20 + 21x + 10x + 7x2 = -50 + -10x + 50 + 10x Combine like terms: 21x + 10x = 31x -20 + 31x + 7x2 = -50 + -10x + 50 + 10x Reorder the terms: -20 + 31x + 7x2 = -50 + 50 + -10x + 10x Combine like terms: -50 + 50 = 0 -20 + 31x + 7x2 = 0 + -10x + 10x -20 + 31x + 7x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -20 + 31x + 7x2 = 0 Factor a trinomial. (-5 + -1x)(4 + -7x) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 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 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Solution
x = {-5, 0.5714285714}
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