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Simplifying (4x + 6)(-7x + -2) = 0 Reorder the terms: (6 + 4x)(-7x + -2) = 0 Reorder the terms: (6 + 4x)(-2 + -7x) = 0 Multiply (6 + 4x) * (-2 + -7x) (6(-2 + -7x) + 4x * (-2 + -7x)) = 0 ((-2 * 6 + -7x * 6) + 4x * (-2 + -7x)) = 0 ((-12 + -42x) + 4x * (-2 + -7x)) = 0 (-12 + -42x + (-2 * 4x + -7x * 4x)) = 0 (-12 + -42x + (-8x + -28x2)) = 0 Combine like terms: -42x + -8x = -50x (-12 + -50x + -28x2) = 0 Solving -12 + -50x + -28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 25x + 14x2) = 0 Factor a trinomial. -2((3 + 2x)(2 + 7x)) = 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 '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Divide each side by '7'. x = -0.2857142857 Simplifying x = -0.2857142857Solution
x = {-1.5, -0.2857142857}
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