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Simplifying (4x + 6)(x + -5) = 0 Reorder the terms: (6 + 4x)(x + -5) = 0 Reorder the terms: (6 + 4x)(-5 + x) = 0 Multiply (6 + 4x) * (-5 + x) (6(-5 + x) + 4x * (-5 + x)) = 0 ((-5 * 6 + x * 6) + 4x * (-5 + x)) = 0 ((-30 + 6x) + 4x * (-5 + x)) = 0 (-30 + 6x + (-5 * 4x + x * 4x)) = 0 (-30 + 6x + (-20x + 4x2)) = 0 Combine like terms: 6x + -20x = -14x (-30 + -14x + 4x2) = 0 Solving -30 + -14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -7x + 2x2) = 0 Factor a trinomial. 2((-3 + -2x)(5 + -1x)) = 0 Ignore the factor 2.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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