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Simplifying
(x + -12)(2x + 3) + -7(4 + -3x) = 0
Reorder the terms:
(-12 + x)(2x + 3) + -7(4 + -3x) = 0
Reorder the terms:
(-12 + x)(3 + 2x) + -7(4 + -3x) = 0
Multiply (-12 + x) * (3 + 2x)
(-12(3 + 2x) + x(3 + 2x)) + -7(4 + -3x) = 0
((3 * -12 + 2x * -12) + x(3 + 2x)) + -7(4 + -3x) = 0
((-36 + -24x) + x(3 + 2x)) + -7(4 + -3x) = 0
(-36 + -24x + (3 * x + 2x * x)) + -7(4 + -3x) = 0
(-36 + -24x + (3x + 2x2)) + -7(4 + -3x) = 0
Combine like terms: -24x + 3x = -21x
(-36 + -21x + 2x2) + -7(4 + -3x) = 0
-36 + -21x + 2x2 + (4 * -7 + -3x * -7) = 0
-36 + -21x + 2x2 + (-28 + 21x) = 0
Reorder the terms:
-36 + -28 + -21x + 21x + 2x2 = 0
Combine like terms: -36 + -28 = -64
-64 + -21x + 21x + 2x2 = 0
Combine like terms: -21x + 21x = 0
-64 + 0 + 2x2 = 0
-64 + 2x2 = 0
Solving
-64 + 2x2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '64' to each side of the equation.
-64 + 64 + 2x2 = 0 + 64
Combine like terms: -64 + 64 = 0
0 + 2x2 = 0 + 64
2x2 = 0 + 64
Combine like terms: 0 + 64 = 64
2x2 = 64
Divide each side by '2'.
x2 = 32
Simplifying
x2 = 32
Take the square root of each side:
x = {-5.656854249, 5.656854249}
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