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Simplifying 2(x + 7) * 3(2x + -5) = 0 Reorder the terms: 2(7 + x) * 3(2x + -5) = 0 Reorder the terms: 2(7 + x) * 3(-5 + 2x) = 0 Reorder the terms for easier multiplication: 2 * 3(7 + x)(-5 + 2x) = 0 Multiply 2 * 3 6(7 + x)(-5 + 2x) = 0 Multiply (7 + x) * (-5 + 2x) 6(7(-5 + 2x) + x(-5 + 2x)) = 0 6((-5 * 7 + 2x * 7) + x(-5 + 2x)) = 0 6((-35 + 14x) + x(-5 + 2x)) = 0 6(-35 + 14x + (-5 * x + 2x * x)) = 0 6(-35 + 14x + (-5x + 2x2)) = 0 Combine like terms: 14x + -5x = 9x 6(-35 + 9x + 2x2) = 0 (-35 * 6 + 9x * 6 + 2x2 * 6) = 0 (-210 + 54x + 12x2) = 0 Solving -210 + 54x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-35 + 9x + 2x2) = 0 Factor a trinomial. 6((-7 + -1x)(5 + -2x)) = 0 Ignore the factor 6.Subproblem 1
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 = -7Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-7, 2.5}
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