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Simplifying 7(2x + -3) + 3 = 6(2x + -3)(2x + -3) Reorder the terms: 7(-3 + 2x) + 3 = 6(2x + -3)(2x + -3) (-3 * 7 + 2x * 7) + 3 = 6(2x + -3)(2x + -3) (-21 + 14x) + 3 = 6(2x + -3)(2x + -3) Reorder the terms: -21 + 3 + 14x = 6(2x + -3)(2x + -3) Combine like terms: -21 + 3 = -18 -18 + 14x = 6(2x + -3)(2x + -3) Reorder the terms: -18 + 14x = 6(-3 + 2x)(2x + -3) Reorder the terms: -18 + 14x = 6(-3 + 2x)(-3 + 2x) Multiply (-3 + 2x) * (-3 + 2x) -18 + 14x = 6(-3(-3 + 2x) + 2x * (-3 + 2x)) -18 + 14x = 6((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) -18 + 14x = 6((9 + -6x) + 2x * (-3 + 2x)) -18 + 14x = 6(9 + -6x + (-3 * 2x + 2x * 2x)) -18 + 14x = 6(9 + -6x + (-6x + 4x2)) Combine like terms: -6x + -6x = -12x -18 + 14x = 6(9 + -12x + 4x2) -18 + 14x = (9 * 6 + -12x * 6 + 4x2 * 6) -18 + 14x = (54 + -72x + 24x2) Solving -18 + 14x = 54 + -72x + 24x2 Solving for variable 'x'. Reorder the terms: -18 + -54 + 14x + 72x + -24x2 = 54 + -72x + 24x2 + -54 + 72x + -24x2 Combine like terms: -18 + -54 = -72 -72 + 14x + 72x + -24x2 = 54 + -72x + 24x2 + -54 + 72x + -24x2 Combine like terms: 14x + 72x = 86x -72 + 86x + -24x2 = 54 + -72x + 24x2 + -54 + 72x + -24x2 Reorder the terms: -72 + 86x + -24x2 = 54 + -54 + -72x + 72x + 24x2 + -24x2 Combine like terms: 54 + -54 = 0 -72 + 86x + -24x2 = 0 + -72x + 72x + 24x2 + -24x2 -72 + 86x + -24x2 = -72x + 72x + 24x2 + -24x2 Combine like terms: -72x + 72x = 0 -72 + 86x + -24x2 = 0 + 24x2 + -24x2 -72 + 86x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -72 + 86x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 43x + -12x2) = 0 Factor a trinomial. 2((-9 + 4x)(4 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 4x)' equal to zero and attempt to solve: Simplifying -9 + 4x = 0 Solving -9 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x = 0 + 9 4x = 0 + 9 Combine like terms: 0 + 9 = 9 4x = 9 Divide each side by '4'. x = 2.25 Simplifying x = 2.25Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {2.25, 1.333333333}
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