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Simplifying (7x + -12)(2x + 2) + -1(4x + 6)(7x + -12) = 0 Reorder the terms: (-12 + 7x)(2x + 2) + -1(4x + 6)(7x + -12) = 0 Reorder the terms: (-12 + 7x)(2 + 2x) + -1(4x + 6)(7x + -12) = 0 Multiply (-12 + 7x) * (2 + 2x) (-12(2 + 2x) + 7x * (2 + 2x)) + -1(4x + 6)(7x + -12) = 0 ((2 * -12 + 2x * -12) + 7x * (2 + 2x)) + -1(4x + 6)(7x + -12) = 0 ((-24 + -24x) + 7x * (2 + 2x)) + -1(4x + 6)(7x + -12) = 0 (-24 + -24x + (2 * 7x + 2x * 7x)) + -1(4x + 6)(7x + -12) = 0 (-24 + -24x + (14x + 14x2)) + -1(4x + 6)(7x + -12) = 0 Combine like terms: -24x + 14x = -10x (-24 + -10x + 14x2) + -1(4x + 6)(7x + -12) = 0 Reorder the terms: -24 + -10x + 14x2 + -1(6 + 4x)(7x + -12) = 0 Reorder the terms: -24 + -10x + 14x2 + -1(6 + 4x)(-12 + 7x) = 0 Multiply (6 + 4x) * (-12 + 7x) -24 + -10x + 14x2 + -1(6(-12 + 7x) + 4x * (-12 + 7x)) = 0 -24 + -10x + 14x2 + -1((-12 * 6 + 7x * 6) + 4x * (-12 + 7x)) = 0 -24 + -10x + 14x2 + -1((-72 + 42x) + 4x * (-12 + 7x)) = 0 -24 + -10x + 14x2 + -1(-72 + 42x + (-12 * 4x + 7x * 4x)) = 0 -24 + -10x + 14x2 + -1(-72 + 42x + (-48x + 28x2)) = 0 Combine like terms: 42x + -48x = -6x -24 + -10x + 14x2 + -1(-72 + -6x + 28x2) = 0 -24 + -10x + 14x2 + (-72 * -1 + -6x * -1 + 28x2 * -1) = 0 -24 + -10x + 14x2 + (72 + 6x + -28x2) = 0 Reorder the terms: -24 + 72 + -10x + 6x + 14x2 + -28x2 = 0 Combine like terms: -24 + 72 = 48 48 + -10x + 6x + 14x2 + -28x2 = 0 Combine like terms: -10x + 6x = -4x 48 + -4x + 14x2 + -28x2 = 0 Combine like terms: 14x2 + -28x2 = -14x2 48 + -4x + -14x2 = 0 Solving 48 + -4x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -2x + -7x2) = 0 Factor a trinomial. 2((12 + -7x)(2 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -7x)' equal to zero and attempt to solve: Simplifying 12 + -7x = 0 Solving 12 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -7x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7x = 0 + -12 -7x = 0 + -12 Combine like terms: 0 + -12 = -12 -7x = -12 Divide each side by '-7'. x = 1.714285714 Simplifying x = 1.714285714Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {1.714285714, -2}
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