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Simplifying (5x + -5)(2x + -7) = 0 Reorder the terms: (-5 + 5x)(2x + -7) = 0 Reorder the terms: (-5 + 5x)(-7 + 2x) = 0 Multiply (-5 + 5x) * (-7 + 2x) (-5(-7 + 2x) + 5x * (-7 + 2x)) = 0 ((-7 * -5 + 2x * -5) + 5x * (-7 + 2x)) = 0 ((35 + -10x) + 5x * (-7 + 2x)) = 0 (35 + -10x + (-7 * 5x + 2x * 5x)) = 0 (35 + -10x + (-35x + 10x2)) = 0 Combine like terms: -10x + -35x = -45x (35 + -45x + 10x2) = 0 Solving 35 + -45x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -9x + 2x2) = 0 Factor a trinomial. 5((1 + -1x)(7 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {1, 3.5}
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