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Simplifying 6x(x + -2) + -3 = 2(x + -2)(x + 2) + -4 Reorder the terms: 6x(-2 + x) + -3 = 2(x + -2)(x + 2) + -4 (-2 * 6x + x * 6x) + -3 = 2(x + -2)(x + 2) + -4 (-12x + 6x2) + -3 = 2(x + -2)(x + 2) + -4 Reorder the terms: -3 + -12x + 6x2 = 2(x + -2)(x + 2) + -4 Reorder the terms: -3 + -12x + 6x2 = 2(-2 + x)(x + 2) + -4 Reorder the terms: -3 + -12x + 6x2 = 2(-2 + x)(2 + x) + -4 Multiply (-2 + x) * (2 + x) -3 + -12x + 6x2 = 2(-2(2 + x) + x(2 + x)) + -4 -3 + -12x + 6x2 = 2((2 * -2 + x * -2) + x(2 + x)) + -4 -3 + -12x + 6x2 = 2((-4 + -2x) + x(2 + x)) + -4 -3 + -12x + 6x2 = 2(-4 + -2x + (2 * x + x * x)) + -4 -3 + -12x + 6x2 = 2(-4 + -2x + (2x + x2)) + -4 Combine like terms: -2x + 2x = 0 -3 + -12x + 6x2 = 2(-4 + 0 + x2) + -4 -3 + -12x + 6x2 = 2(-4 + x2) + -4 -3 + -12x + 6x2 = (-4 * 2 + x2 * 2) + -4 -3 + -12x + 6x2 = (-8 + 2x2) + -4 Reorder the terms: -3 + -12x + 6x2 = -8 + -4 + 2x2 Combine like terms: -8 + -4 = -12 -3 + -12x + 6x2 = -12 + 2x2 Solving -3 + -12x + 6x2 = -12 + 2x2 Solving for variable 'x'. Reorder the terms: -3 + 12 + -12x + 6x2 + -2x2 = -12 + 2x2 + 12 + -2x2 Combine like terms: -3 + 12 = 9 9 + -12x + 6x2 + -2x2 = -12 + 2x2 + 12 + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 9 + -12x + 4x2 = -12 + 2x2 + 12 + -2x2 Reorder the terms: 9 + -12x + 4x2 = -12 + 12 + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 9 + -12x + 4x2 = 0 + 2x2 + -2x2 9 + -12x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + -12x + 4x2 = 0 Factor a trinomial. (3 + -2x)(3 + -2x) = 0Subproblem 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 '(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 = 1.5Solution
x = {1.5, 1.5}
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