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Simplifying (4x + -3)(4x + -3) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: (-3 + 4x)(4x + -3) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: (-3 + 4x)(-3 + 4x) + -1(2x + 5)(2x + 5) = 0 Multiply (-3 + 4x) * (-3 + 4x) (-3(-3 + 4x) + 4x * (-3 + 4x)) + -1(2x + 5)(2x + 5) = 0 ((-3 * -3 + 4x * -3) + 4x * (-3 + 4x)) + -1(2x + 5)(2x + 5) = 0 ((9 + -12x) + 4x * (-3 + 4x)) + -1(2x + 5)(2x + 5) = 0 (9 + -12x + (-3 * 4x + 4x * 4x)) + -1(2x + 5)(2x + 5) = 0 (9 + -12x + (-12x + 16x2)) + -1(2x + 5)(2x + 5) = 0 Combine like terms: -12x + -12x = -24x (9 + -24x + 16x2) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: 9 + -24x + 16x2 + -1(5 + 2x)(2x + 5) = 0 Reorder the terms: 9 + -24x + 16x2 + -1(5 + 2x)(5 + 2x) = 0 Multiply (5 + 2x) * (5 + 2x) 9 + -24x + 16x2 + -1(5(5 + 2x) + 2x * (5 + 2x)) = 0 9 + -24x + 16x2 + -1((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 0 9 + -24x + 16x2 + -1((25 + 10x) + 2x * (5 + 2x)) = 0 9 + -24x + 16x2 + -1(25 + 10x + (5 * 2x + 2x * 2x)) = 0 9 + -24x + 16x2 + -1(25 + 10x + (10x + 4x2)) = 0 Combine like terms: 10x + 10x = 20x 9 + -24x + 16x2 + -1(25 + 20x + 4x2) = 0 9 + -24x + 16x2 + (25 * -1 + 20x * -1 + 4x2 * -1) = 0 9 + -24x + 16x2 + (-25 + -20x + -4x2) = 0 Reorder the terms: 9 + -25 + -24x + -20x + 16x2 + -4x2 = 0 Combine like terms: 9 + -25 = -16 -16 + -24x + -20x + 16x2 + -4x2 = 0 Combine like terms: -24x + -20x = -44x -16 + -44x + 16x2 + -4x2 = 0 Combine like terms: 16x2 + -4x2 = 12x2 -16 + -44x + 12x2 = 0 Solving -16 + -44x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -11x + 3x2) = 0 Factor a trinomial. 4((-1 + -3x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.3333333333, 4}
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