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Simplifying 2(-2x + 1) * 2(6x + 5) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Reorder the terms: 2(1 + -2x) * 2(6x + 5) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Reorder the terms: 2(1 + -2x) * 2(5 + 6x) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Reorder the terms for easier multiplication: 2 * 2(1 + -2x)(5 + 6x) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Multiply 2 * 2 4(1 + -2x)(5 + 6x) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Multiply (1 + -2x) * (5 + 6x) 4(1(5 + 6x) + -2x * (5 + 6x)) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x 4((5 * 1 + 6x * 1) + -2x * (5 + 6x)) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x 4((5 + 6x) + -2x * (5 + 6x)) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x 4(5 + 6x + (5 * -2x + 6x * -2x)) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x 4(5 + 6x + (-10x + -12x2)) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Combine like terms: 6x + -10x = -4x 4(5 + -4x + -12x2) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x (5 * 4 + -4x * 4 + -12x2 * 4) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x (20 + -16x + -48x2) + x + 1 = -5(-2x + 3) + -2(3x + -14) + x Reorder the terms: 20 + 1 + -16x + x + -48x2 = -5(-2x + 3) + -2(3x + -14) + x Combine like terms: 20 + 1 = 21 21 + -16x + x + -48x2 = -5(-2x + 3) + -2(3x + -14) + x Combine like terms: -16x + x = -15x 21 + -15x + -48x2 = -5(-2x + 3) + -2(3x + -14) + x Reorder the terms: 21 + -15x + -48x2 = -5(3 + -2x) + -2(3x + -14) + x 21 + -15x + -48x2 = (3 * -5 + -2x * -5) + -2(3x + -14) + x 21 + -15x + -48x2 = (-15 + 10x) + -2(3x + -14) + x Reorder the terms: 21 + -15x + -48x2 = -15 + 10x + -2(-14 + 3x) + x 21 + -15x + -48x2 = -15 + 10x + (-14 * -2 + 3x * -2) + x 21 + -15x + -48x2 = -15 + 10x + (28 + -6x) + x Reorder the terms: 21 + -15x + -48x2 = -15 + 28 + 10x + -6x + x Combine like terms: -15 + 28 = 13 21 + -15x + -48x2 = 13 + 10x + -6x + x Combine like terms: 10x + -6x = 4x 21 + -15x + -48x2 = 13 + 4x + x Combine like terms: 4x + x = 5x 21 + -15x + -48x2 = 13 + 5x Solving 21 + -15x + -48x2 = 13 + 5x Solving for variable 'x'. Reorder the terms: 21 + -13 + -15x + -5x + -48x2 = 13 + 5x + -13 + -5x Combine like terms: 21 + -13 = 8 8 + -15x + -5x + -48x2 = 13 + 5x + -13 + -5x Combine like terms: -15x + -5x = -20x 8 + -20x + -48x2 = 13 + 5x + -13 + -5x Reorder the terms: 8 + -20x + -48x2 = 13 + -13 + 5x + -5x Combine like terms: 13 + -13 = 0 8 + -20x + -48x2 = 0 + 5x + -5x 8 + -20x + -48x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -20x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -5x + -12x2) = 0 Factor a trinomial. 4((1 + -4x)(2 + 3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {0.25, -0.6666666667}
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