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Simplifying 4(2x + 3)(x + -5) = 0 Reorder the terms: 4(3 + 2x)(x + -5) = 0 Reorder the terms: 4(3 + 2x)(-5 + x) = 0 Multiply (3 + 2x) * (-5 + x) 4(3(-5 + x) + 2x * (-5 + x)) = 0 4((-5 * 3 + x * 3) + 2x * (-5 + x)) = 0 4((-15 + 3x) + 2x * (-5 + x)) = 0 4(-15 + 3x + (-5 * 2x + x * 2x)) = 0 4(-15 + 3x + (-10x + 2x2)) = 0 Combine like terms: 3x + -10x = -7x 4(-15 + -7x + 2x2) = 0 (-15 * 4 + -7x * 4 + 2x2 * 4) = 0 (-60 + -28x + 8x2) = 0 Solving -60 + -28x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -7x + 2x2) = 0 Factor a trinomial. 4((-3 + -2x)(5 + -1x)) = 0 Ignore the factor 4.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 '(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 = 5Solution
x = {-1.5, 5}
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