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Simplifying 0 = -5(x + -7)(2x + 3) Reorder the terms: 0 = -5(-7 + x)(2x + 3) Reorder the terms: 0 = -5(-7 + x)(3 + 2x) Multiply (-7 + x) * (3 + 2x) 0 = -5(-7(3 + 2x) + x(3 + 2x)) 0 = -5((3 * -7 + 2x * -7) + x(3 + 2x)) 0 = -5((-21 + -14x) + x(3 + 2x)) 0 = -5(-21 + -14x + (3 * x + 2x * x)) 0 = -5(-21 + -14x + (3x + 2x2)) Combine like terms: -14x + 3x = -11x 0 = -5(-21 + -11x + 2x2) 0 = (-21 * -5 + -11x * -5 + 2x2 * -5) 0 = (105 + 55x + -10x2) Solving 0 = 105 + 55x + -10x2 Solving for variable 'x'. Combine like terms: 0 + -105 = -105 -105 + -55x + 10x2 = 105 + 55x + -10x2 + -105 + -55x + 10x2 Reorder the terms: -105 + -55x + 10x2 = 105 + -105 + 55x + -55x + -10x2 + 10x2 Combine like terms: 105 + -105 = 0 -105 + -55x + 10x2 = 0 + 55x + -55x + -10x2 + 10x2 -105 + -55x + 10x2 = 55x + -55x + -10x2 + 10x2 Combine like terms: 55x + -55x = 0 -105 + -55x + 10x2 = 0 + -10x2 + 10x2 -105 + -55x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -105 + -55x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + -11x + 2x2) = 0 Factor a trinomial. 5((-3 + -2x)(7 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-1.5, 7}
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